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Journal of Dezhou University

Direct Measurement of the Wigner Function of a Single Trapped Ion

Zhang Su-zhen

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

In the scheme,the trapped ion is driven by two laser beams with different frequencies tuned to the first lower and upper vibrational sidebands,the ion interacts with the leaser,then we could obtain the Wigner function by detecting the internal state of the ion.

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In this paper, a procedure is proposed for measuring Wigner characteristic function for motion of a single trapped ion. In the scheme, the trapped ion is driven by two laser beams with different frequencies tuned to the first lower and upper vibrational sidebands, respectively. Unlike other previous scheme, our scheme does not require the displacement of the external state before the ion-laser interaction and thus our scheme might be more simple and feasible. The scheme can also be used to prepare the motional Schrodinger cat states and entangled coherent states.
We propose a scheme for generating superpositions of coherent states for both the centre-of-mass and relative vibrational modes of two trapped ions. In the proposed scheme two trapped ions are driven by two laser beams dispersively tuned to the first lower- and upper-vibrational sideband transitions, respectively. Under certain conditions, the measurement of the internal states leaves one vibrational mode in a superposition of two coherent states. Entangled coherent states for these two vibrational modes can also be generated. The scheme can be used to measure the Wigner function of one vibrational mode given that the other mode is initially in the vacuum state.